There has been used a power supply system configured such that a chargeable secondary battery supplies a load with electric power and the secondary battery can also be charged as required while the load is in operation. Representatively, hybrid vehicles, electric vehicles and the like including as a driving force source an electric motor driven by a secondary battery have such power supply systems mounted therein. In these power supply systems, the secondary battery's stored electric power is used as electric power driving the electric motor serving as the driving force source, and electric power generated when the electric motor regenerates electric power, electric power generated by an electric power generator as an engine rotates, and the like charge the secondary battery. Typically, such power supply systems require a device estimating the secondary battery's state to precisely obtain a state of charge (SOC) relative to its fully charged state.
For hybrid vehicles in particular, it is necessary that the secondary battery have its state of charge controlled to be approximately intermediate between its fully charged state (100%) and its completely uncharged state (0%), i.e., 50 to 60%, so that the secondary battery can receive regenerated electric power and also supply the electric motor with electric power immediately as required.
Furthermore, over-discharging or overcharging a secondary battery may degrade the battery's performance and reduce its life. As such, when an intermediate SOC is set as a target for control, as described above, and a secondary battery is accordingly charged/discharged repeatedly in its use, the secondary battery's amount of charge is monitored sequentially and charging/discharging the secondary battery is controlled to restrict overcharging/over-discharging the secondary battery. In this regard also, it is significantly necessary to precisely estimate the secondary battery's state.
When a secondary battery's state is estimated, representatively, its state of charge is estimated. For example, patent document 1 (Japanese Patent Laying-open No. 2005-37230) discloses a technique to estimate from a value of a cumulative current of a battery how the battery varies in SOC. In particular, patent document 1 describes that a current sensor measures the battery's current and in parallel therewith an operation is performed to obtain an estimated charged/discharged current, and an operation is performed to obtain the battery's current to obtain a measured SOC, while the estimated charged/discharged current is accumulated to obtain an estimated SOC. A difference between the estimated SOC and the measured SOC is obtained and how the difference in SOC varies with time is accumulated to obtain a cumulative SOC value, and when the cumulative SOC value is equal to or larger than a predetermined value in comparison with an initial value, that the battery is degraded is detected.
In patent document 1, however, the estimated charged/discharged current is obtained in accordance with a relational expression based on Ohm's law between internal resistance, the battery's voltage and the battery's input. It is thus difficult to precisely estimate the battery's internal state from an electrochemical reaction.
Furthermore, patent document 2 (Japanese Patent Laying-open No. 2004-178848) discloses a device estimating a state of charge of a secondary battery, that is configured such that an adaptive digital filter is used to estimate no load voltage (OCV) from a value of the secondary battery's current as measured and that of a terminal's voltage as measured and a state of charge is estimated in accordance with a previously obtained relationship between no load voltage and a state of charge.
This device estimating a state of charge of a secondary battery, however, employs a low pass filter as the secondary battery's internal equivalent circuit model, and it is thus difficult to precisely estimate the secondary battery's internal behavior involving the diffusion of a reaction involved material contributing to an electrochemical reaction.
Accordingly, non-patent document 1 (W. B. Gu and C. Y. Wang, THERMAL-ELECTROCHEMICAL COUPLED MODELING OF A LITHIUM-ION CELL, ECS Proceedings Vol. 99-25 (1), 2000, ECS, pp. 748-762) discusses a battery model employing an expression of an electrochemical reaction internal to a lithium battery and reports that a characteristic can be represented with high precision in comparison with an actual battery. In particular, non-patent document 1 indicates that the secondary battery's no load voltage depends on a local SOC obtained at an electrode's interface with an electrolytic solution (a surface of an active material) and as a result the battery's voltage in relaxation is governed by diffusion of lithium depending on how lithium is distributed in concentration in an active material. In particular, the document discloses that the diffusion of the reaction involved material (lithium) in the active material is governed by a diffusion equation of spherical coordinates handling the active material as a sphere and a diffusion rate of a material governed by a diffusion coefficient in a diffusion process.
In estimating a secondary battery's state, as indicated in patent documents 1 and 2, as described above, the secondary battery's internal state will estimated by a macro equivalent model with the secondary battery's voltage and current serving as an input and an output, and it is difficult to provide estimation with high precision based on the secondary battery's internal state involving the reaction involved material's diffusion.
On the other hand, as disclosed in non-patent document 1, if the reaction involved material's diffusion is represented by a diffusion equation, as based on the battery's internal electrochemical reaction, and the battery's open circuit voltage depends on a local SOC obtained at an electrode-electrolytic solution interface (a surface of an active material), then while the battery model will be non-linear, the battery's state can be estimated with higher precision. However, an analysis provided in accordance with the model disclosed in non-patent document 1 involves a significantly large operating load and it is thus difficult for example to mount it in an actual device and estimate a state on line when the secondary battery is used.